To determine the mass of magnesium chloride ([tex]\( MgCl_2 \)[/tex]) formed when 20.0 grams of solid magnesium react with 50.0 grams of chlorine gas, we'll follow these steps:
1. Calculate Moles of Magnesium (Mg):
- The molar mass of magnesium ([tex]\( Mg \)[/tex]) is [tex]\( 24.305 \)[/tex] grams per mole.
- Mass of magnesium provided is [tex]\( 20.0 \)[/tex] grams.
[tex]\[
\text{Moles of Mg} = \frac{\text{Mass of Mg}}{\text{Molar Mass of Mg}} = \frac{20.0 \, \text{g}}{24.305 \, \text{g/mol}} \approx 0.8229 \, \text{moles}
\][/tex]
2. Calculate Moles of Chlorine Gas (Cl[tex]\(_2\)[/tex]):
- The molar mass of chlorine gas ([tex]\( Cl_2 \)[/tex]) is [tex]\( 70.906 \)[/tex] grams per mole.
- Mass of chlorine gas provided is [tex]\( 50.0 \)[/tex] grams.
[tex]\[
\text{Moles of Cl}_2 = \frac{\text{Mass of Cl}_2}{\text{Molar Mass of Cl}_2} = \frac{50.0 \, \text{g}}{70.906 \, \text{g/mol}} \approx 0.7052 \, \text{moles}
\][/tex]
3. Determine the Limiting Reactant:
The balanced chemical equation [tex]\( Mg + Cl_2 \rightarrow MgCl_2 \)[/tex] shows that magnesium and chlorine gas react in a 1:1 molar ratio. Thus, since:
- Moles of [tex]\( Mg \)[/tex] available: [tex]\( 0.8229 \)[/tex] moles
- Moles of [tex]\( Cl_2 \)[/tex] available: [tex]\( 0.7052 \)[/tex] moles
The limiting reactant is [tex]\( Cl_2 \)[/tex] because there are fewer moles of chlorine gas compared to the moles of magnesium.
4. Determine the Moles of [tex]\( MgCl_2 \)[/tex] Formed:
Since the chlorine gas is the limiting reactant, the moles of [tex]\( MgCl_2 \)[/tex] formed will be equal to the moles of chlorine gas available.
[tex]\[
\text{Moles of } MgCl_2 = \text{Moles of } Cl_2 \approx 0.7052 \, \text{moles}
\][/tex]
5. Calculate the Mass of [tex]\( MgCl_2 \)[/tex] Formed:
- The molar mass of magnesium chloride ([tex]\( MgCl_2 \)[/tex]) is [tex]\( 95.211 \)[/tex] grams per mole.
[tex]\[
\text{Mass of } MgCl_2 = \text{Moles of } MgCl_2 \times \text{Molar Mass of } MgCl_2 = 0.7052 \, \text{moles} \times 95.211 \, \text{g/mol} \approx 67.14 \, \text{grams}
\][/tex]
Therefore, the mass of solid magnesium chloride ([tex]\( MgCl_2 \)[/tex]) formed during the reaction is approximately [tex]\( 67.14 \)[/tex] grams.
